Question: Simplify to lowest terms. $\dfrac{135}{150}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 135 and 150? $135 = 3\cdot3\cdot3\cdot5$ $150 = 2\cdot3\cdot5\cdot5$ $\mbox{GCD}(135, 150) = 3\cdot5 = 15$ $\dfrac{135}{150} = \dfrac{9 \cdot 15}{ 10\cdot 15}$ $\hphantom{\dfrac{135}{150}} = \dfrac{9}{10} \cdot \dfrac{15}{15}$ $\hphantom{\dfrac{135}{150}} = \dfrac{9}{10} \cdot 1$ $\hphantom{\dfrac{135}{150}} = \dfrac{9}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{135}{150}= \dfrac{3\cdot45}{3\cdot50}= \dfrac{3\cdot 5\cdot9}{3\cdot 5\cdot10}= \dfrac{9}{10}$